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# The Derren Brown Coin Flipping Scam

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Age 16 to 18

Challenge Level

The illusionist Derren Brown famously flipped a coin continuously on camera until he obtained 10 heads in a row. He then simply showed the last 10 flips of the film on TV, claiming that he influenced the outcome of each flip to get 10 heads first time.

Lots of ideas concerning risk and probability enter into this scam, and it is great for discussion. Why not consider these short questions as starting points? You will need to quantify carefully any aspects which seem vague or unclear.

1. What was the chance of DB completing the coin scam on the first attempt?

2. How many flips would you expect DB to have made before making 10 consecutive heads?

3. I've tried to repeat the DB coin experiment and have flipped my coin 5000 times with no run of 10 heads and just got another tail. How many more flips do I expect to need to make to make 10 consecutive heads?

4. My friend wants to replicate the coin flipping scam. How much time should she put aside to be reasonably confident of completing the challenge?

5. I've been flipping coins all day without success. I've just got a tail and there is 10 minutes of the school day left. If I make 1 flip per second, what chance have I got of achieving the 10 consecutive Heads before the end of the day?

6. My friend in the Technology department has worked out a way of slightly doctoring the coin to give a 55% chance of heads on each throw instead of 50%. How helpful will this small change in probabilities be to our chances of success?

7. What physical effects might bias the results or affect the outcome?

8. DB took about 10 hours to get the 10 heads in succession, which was longer than might be expected. How unlucky was he to have taken this long? Very unlucky? Quite unlucky? How might you quantify this statement?

9. Suppose that everyone in Britain flipped a coin until they obtained 10 consecutive heads. What range would you estimate the shortest number of flips to be in? How about for the longest number of flips?

10. Imagine that someone wanted to try to replicate this stunt, only this time stopping with a greater number of consecutive heads. For what number of consecutive heads would this be practically feasible?